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 A119786 Numerator of the product of the n-th triangular number and the n-th harmonic number. 1
 1, 9, 11, 125, 137, 1029, 363, 6849, 7129, 81191, 83711, 1118273, 1145993, 1171733, 1195757, 41421503, 42142223, 813635157, 275295799, 279175675, 56574159, 439143531, 1332950097, 33695573875, 34052522467, 309561680403, 312536252003, 9146733078187 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Also numerator of the sum of all matrix elements of n X n matrix M[i,j] = i/j, i,j=1..n. p^3 divides a(p-1) for prime p>3, p^3 divides a(p^2-1) for prime p>3, p^3 divides a(p^3-1) for prime p>3, p^3 divides a(p^4-1) for prime p>3, ... LINKS Alois P. Heinz, Table of n, a(n) for n = 1..1000 FORMULA a(n) = numerator[Sum[i,{i, 1, n}] * Sum[1/j,{j, 1, n}]] = numerator[n(n+1)/2 * Sum[1/i,{i, 1, n}]] = numerator[A000217(n) * (A001008(n)/A002805(n))]. Also a(n) = numerator[Sum[Sum[i/j,{i, 1, n}],{j, 1, n}]]. MAPLE a:= n-> numer(add(add(i/j, j=1..n), i=1..n)): seq(a(n), n=1..30); # Zerinvary Lajos, Jun 14 2007 # second Maple program: h:= proc(n) h(n):= 1/n +`if`(n=1, 0, h(n-1)) end: t:= proc(n) t(n):= n +`if`(n=1, 0, t(n-1)) end: a:= n-> numer(h(n)*t(n)): seq(a(n), n=1..30); # Alois P. Heinz, May 24 2013 MATHEMATICA Numerator[Table[n(n+1)/2*Sum[1/i, {i, 1, n}], {n, 1, 50}]]. Numerator[Table[Sum[Sum[i/j, {i, 1, n}], {j, 1, n}], {n, 1, 50}]]. Table[(n(n+1))/2 HarmonicNumber[n], {n, 30}]//Numerator (* Harvey P. Dale, May 06 2018 *) CROSSREFS Cf. A000217, A001008, A002805. Sequence in context: A359457 A027727 A019328 * A147429 A147461 A146366 Adjacent sequences: A119783 A119784 A119785 * A119787 A119788 A119789 KEYWORD frac,nonn AUTHOR Alexander Adamchuk, Jun 25 2006, Jul 12 2006 EXTENSIONS Edited by N. J. A. Sloane at the suggestion of Andrew S. Plewe, May 27 2007 STATUS approved

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Last modified June 7 00:08 EDT 2023. Contains 363151 sequences. (Running on oeis4.)